ETF Flow Analysis - MathWorks

Statistical Analysis of ETF Flows,

Prices, and Premiums

Aleksander Sobczyk

iShares Global Investments & Research

BlackRock

Matlab Computational Finance Conference

New York

April 9th, 2014

iS-12030 FOR INSTITUTIONAL USE ONLY - NOT FOR PUBLIC DISTRIBUTION

Agenda

Rapid growth of exchange-traded funds (ETFs) has generated considerable interest in the dynamics of

flows, prices, and premiums:

Despite over $2 trillion of AUM world-wide as of 2013, there is not to our knowledge any previous systematic

statistical analysis of ETF flows

As ETFs are used by hedge funds and other sophisticated investors to quickly and cheaply express their views

across asset classes and regions, flows could be very informative about changes in investor sentiment

Concerns have been raised around ETF role in global financial markets, particularly about premiums and discounts

to NAV, as well as risks for overall market liquidity

Analyzing data that is increasing both in size and complexity (intra-day ETF prices and premiums, ETF taxonomy

and classifications, fund holdings information, auxiliary datasets, etc.) requires state-of-the-art tools like Matlab

Objectives:

Part One: Understand dynamics of ETF flows:

Are flows predictable? At what horizons? What drives flow dynamics?

How are flows related to past flows and returns within an asset class? Across asset classes?

Can flows or sentiment predict returns?

Part Two: Analyze the role of ETFs in the global financial markets:

Clarify common misconceptions about premiums and discounts to NAV.

Provide canonical framework to analyze liquidity and price discovery functions of ETFs.

iS-12030 FOR INSTITUTIONAL USE ONLY - NOT FOR PUBLIC DISTRIBUTION 2

Part One: Statistical Analysis of ETF Flows


BlackRock

How to Define ETF Flows?

Unlike a traditional mutual fund, purchases/sales of ETFs do not necessarily require investors to interact with the

fund; offering lower costs and tax efficiency; transactions can also occur throughout the day.

While ETFs trade intraday on organized exchanges, like equities, the creation-redemption mechanism allows

additional ETF supply/demand through primary market transactions beyond visible secondary market.

Authorized

Participant ETF Issuer

Basket of underlying securities

ETF units

Creation Process: Authorized Participant delivers a basket of underlying securities to issuer

who in turn delivers the ETF units

Total ETF Flow in a month (or week) with T trading days

= Total Creations Minus Redemptions

= S i=1..T days (Shares Outi – Shares Outi-1) * NAVi


Global ETF Flows and Assets


Source: BlackRock “ETP Landscape” as of December 31, 2013

5

Predictability of Flows Within Asset Classes

Are flows predictable?

Simplest approach is to look at autocorrelation in scaled flows within an asset class

Examine weekly and monthly frequencies as the daily data is too noisy

Consistent patterns emerge:

Equity flows are not autocorrelated, indicating little persistence over weekly or monthly horizons

However, at weekly and monthly frequencies, both commodity and fixed income flows are strongly positive

autocorrelated

Autocorrelation is stronger during the period of the financial crisis suggesting that investors sentiment tended to be

persistent from week to week with no evidence of contrarian behavior


January 2005 - July 2013

Flow Change (%) Descriptive Statistics by Asset Class

Asset Class Mean Median Std Dev 1st Autocorr

Equity 0.07 0.05 0.12 -0.05

Fixed Income 0.15 0.14 0.12 0.26**

Commodities 0.16 0.09 0.42 0.24*

Monthly Exchange Traded Product (ETP) Flow Changes All US-domiciled ETPs, January 2005 – July 2013

Flow Change (%) = (1 / T) Flowk / AUMk-1

Source: Bloomberg, Thomson Reuters, BlackRock, as at July 31, 2013

05 06 07 08 09 10 11 12 13 14-0.5

0

0.5Equity ETPs

Year

Flo

w C

hange (

%)

05 06 07 08 09 10 11 12 13 14-0.5

0

0.5

1Fixed Income ETPs

Year

Flo

w C

hange (

%)

05 06 07 08 09 10 11 12 13 14-2

0

2

4Commodities ETPs

Year

Flo

w C

hange (

%)

*** Denotes statistical signif icance at 0.1%

** Denotes statistical signif icance at 1%

* Denotes statistical signif icance at 5%


Weekly ETP Flow Changes All US-domiciled ETPs, January 2005 – July 2013

Flow Change (%) = (1 / T) Flowk / AUMk-1

Source: Bloomberg, Thomson Reuters, BlackRock , as at July 31, 2013

January 2005 - July 2013

Flow Change (%) Descriptive Statistics by Asset Class


Equity 0.07 0.05 0.23 -0.03

Fixed Income 0.15 0.14 0.20 0.17***

Commodities 0.13 0.07 0.38 0.36***

05 06 07 08 09 10 11 12 13 14-1

0

1

2Equity ETPs

Year

Flo

w C

hange (

%)

05 06 07 08 09 10 11 12 13 14-2

-1

0

1

2Fixed Income ETPs

Year

Flo

w C

hange (

%)

05 06 07 08 09 10 11 12 13 14-2

0

2

4Commodities ETPs

Year

Flo

w C

hange (

%)

*** Denotes statistical signif icance at 0.1%

** Denotes statistical signif icance at 1%

* Denotes statistical signif icance at 5%


Predictability of Flows Across Asset Classes

Are flows predictable? What drives flows?

Autocorrelation within an asset class is useful but does not shed light on cross-asset or lead-lag relationships

We use autoregression (AR) framework to model flows within a given asset class as a function of past flows and past

returns

Extend to VAR model to account for cross-asset class effects (note: dimensionality is a challenge)

We include year-end effects as this seasonality is important in driving flows

Consistent results

Equity

Equity flows at weekly or monthly horizons are strongly correlated with contemporaneous returns, which is consistent

with anecdotal evidence

Fixed Income

At weekly and monthly frequencies, both fixed income and commodity flows are strongly positive correlated with lagged

flows

Model fit is especially strong post the financial crisis


Equities - Monthly

Dependent Variable =

Independent Flow Change (%)

Variable: AR(1) AR(1) AR(2)

Constant 0.0005

(4.80)

0.0006

(4.88)

0.0007

(4.59)

Flow

Change (%)

Flow Lag 1 Month -0.0665

(0.70)

-0.0649

(0.66)

Flow Lag 2 Months -0.0690

(0.69)

Asset Class

Return

(Russell

3000 Index)

Return Lag 0

(Contemporaneous)

0.0037

(1.62)

Return Lag 1 Month -0.0033

(1.42)

-0.0034

(1.31)

Return Lag 2 Months -0.0023

(0.90)

Dummy is_year_end 0.0014

(3.45)

0.0014

(3.57)

0.0015

(3.57)

Adjusted R-square 11.80% 11.18% 11.21%

Observations 101 101 100

Autoregressive Models – Equity ETP Flows All Equity US-domiciled ETPs, January 2005 – July 2013

Flows vs. Lagged Flows and Lagged Russell 3000 Index Returns


Equities - Weekly



Variable AR(1) AR(1) AR(2)

Constant 0.0005

(4.95)

0.0006

(5.05)

0.0006

(4.69)

Flow

Change (%)

Flow Lag 1 Week -0.0451

(0.90)

-0.0442

(0.87)

Flow Lag 2 Weeks 0.0358

(0.71)

Asset Class

Return

(Russell

3000 Index)

Return Lag 0

(Contemporaneous)

0.0254

(6.91)

Return Lag 1 Week -0.0041

(1.00)

-0.0035

(0.84)

Return Lag 2 Weeks 0.0019

(0.46)


(3.16)

0.0014

(3.44)

0.0013

(3.28)



Values:

Beta

(|T-Stat|) Each column is a autoregressive model; shading indicates statistical significance at 1% level

Strong contemporaneous correlation between weekly equity ETP flows and R3K returns


Autoregressive Models – Fixed Income All Fixed Income US-domiciled ETPs, January 2005 – July 2013


Flows vs. Lagged Flows and Lagged Barclays AGG Index Returns

Fixed Income - Weekly




Constant 0.0015

(15.10)

0.0013

(10.26)

0.0012

(8.58)

Flow

Change (%)

Flow Lag 1 Week 0.1671

(3.58)

0.1413

(3.00)

Flow Lag 2 Weeks 0.0579

(1.24)

Asset Class

Return

(Barclays

Aggregate

Index)

Return Lag 0

(Contemporaneous)

-0.0150

(0.77)

Return Lag 1 Week 0.0018

(0.09)

0.0016

(0.08)


(1.20)

Dummy is_year_end -0.0003

(0.74)

-0.0002

(0.68)

-0.0002

(0.60)

Adjusted R-square -0.20% 2.28% 1.99%


Fixed Income -

Monthly




Constant 0.0014

(11.01)

0.0010

(5.67)

0.0011

(5.22)

Flow

Change (%)

Flow Lag 1 Month 0.2399

(2.56)

0.1323

(1.41)

Flow Lag 2 Months 0.0441

(0.48)

Asset Class

Return

(Barclays

Aggregate

Index)

Return Lag 0

(Contemporaneous)

0.0096

(0.79)

Return Lag 1 Month 0.0213

(1.82)

0.0262

(2.38)

Return Lag 2 Months 0.0015

(0.13)

Dummy is_year_end -0.0003

(0.71)

-0.0004

(1.00)

-0.0004

(0.98)

Adjusted R-square -0.87% 7.38% 4.76%


Values:

Beta

(|T-Stat|) Strong autocorrelation in fixed income flows at both monthly and weekly horizons


Vector Autoregressive Model (VAR) All US-domiciled ETPs, January 2005 – July 2013


Values:

Beta

(|T-Stat|)

Dependent Variable:

1- Week Lagged

Independent Variable:

Equity

Flow FI Flow Cmd Flow

Russell

3000

Barclays

AGG

TR/J CRB

Index

Flow

Change

(%) Lag

1 Week

Equity -0.0238

(0.48)

-0.1266

(2.90)

-0.1455

(2.04)

-1.9798

(3.33)

0.1171

(1.12)

-2.2412

(3.77)

Fixed

Income

-0.0193

(0.36)

0.1679

(3.61)

0.0302

(0.40)

-0.0173

(0.03)

-0.0170

(0.15)

0.7562

(1.18)

Cmd -0.0019

(0.07)

0.0275

(1.10)

0.3343

(8.15)

-0.8686

(2.53)

-0.0013

(0.02)

0.0567

(0.17)

Asset

Returns

Lag 1

Week

Russell

3000

-0.0050

(1.07)

-0.0013

(0.31)

0.0090

(1.35)

-0.0105

(0.19)

0.0356

(3.62)

0.0849

(1.52)

Barclays

AGG

-0.0316

(1.43)

0.0016

(0.08)

0.0576

(1.81)

0.0621

(0.23)

-0.0514

(1.10)

-0.3000

(1.13)

TR/J CRB

Index

0.0003

(0.07)

0.0081

(2.10)

0.0042

(0.66)

0.0097

(0.18)

0.0060

(0.64)

-0.0696

(1.31)

Weekly 6-Dimensional VAR(1) Model solved in Matlab (using vgxvarx):

Strong autocorrelation in fixed income and commodity ETP flows

Equity ETP flows are drivers of fixed income and commodity flows

Interesting reversal pattern of Russell 3000 index on equity ETP flows, consistent with price

pressure hypothesis


Equity ETP Flows and Russell 3000 Index Reversal All Equity US-domiciled ETPs, January 2005 – July 2013


Russell 3000 Index Returns vs. Lagged Flows

Equities - Monthly


Independent Russell 3000 Index Return


Constant 0.0031

(0.65)

0.0110

(2.16)

0.0190

(3.39)

Flow

Change (%)

Flow Lag 1 Month -13.4674

(3.50)

-14.9108

(3.87)

Flow Lag 2 Months -9.5286

(2.43)

Russell

3000 Index

Return

Return Lag 1 Month 0.2329

(2.36)

0.2879

(3.04)

0.2531

(2.52)

Return Lag 2 Months -0.0769

(0.78)


(0.80)

0.0206

(1.27)

0.0231

(1.45)



Equities - Weekly


Independent Russell 3000 Index Return


Constant 0.0010

(0.75)

0.0021

(1.54)

0.0024

(1.71)

Flow

Change (%)

Flow Lag 1 Week -2.1898

(3.59)

-2.1521

(3.53)

Flow Lag 2 Weeks -0.6374

(1.04)

Russell

3000 Index

Return

Return Lag 1 Week -0.0593

(1.25)

-0.0055

(0.11)

-0.0115

(0.23)


(1.50)


(0.81)

0.0071

(1.47)

0.0074

(1.53)



Russell 3000 Index reversal persistent at both monthly and weekly horizon

This effect is consistent with price pressure hypothesis


Risk Flow Sentiment Measure

Are flows indicative of investor sentiment?

With over $2 trillion in worldwide AUM, ETPs are used by sophisticated investors to express their views across asset

classes and regions

We derived a simple metric that captures shifts in investor sentiment as expressed via primary ETP flows

BlackRock Risk Flow Sentiment measure:

BlackRock Risk Flow Sentiment measure sorts ETPs within each asset class based on risk of each fund

Risk Flow Sentiment is then defined as total dollar inflows/outflows for the riskers group of ETPs less those of safer

group, scaled by the dispersion of all flows

Our research shows that over longer horizons (i.e. monthly), Risk Flow Sentiment exhibits greater persistence than

raw flows alone, consistent with the idea that composition of flows is indicative of investor sentiment

BlackRock Risk Flow Sentiment measure has been regularly included in the ETF Landscape starting in July 2013

Source: BlackRock , as at July 31, 2013


BlackRock Risk Flow Sentiment Measure Introduced in July’s 2013 Issue of ETP Landscape

BlackRock Risk Flow Sentiment Measure is

derived from raw monthly risk flow metric as deviation from one-year moving average


Source: BlackRock “ETP Landscape”

as of July 31, 2013

15

Monthly Sentiment Flows Statistics (01/05 - 07/13)


Equities -6.17 -6.24 26.05 0.20*

Fixed Income -6.34 -3.91 11.25 0.43***

Commodities -1.74 -1.75 5.70 0.21*

Risk Flow Sentiment exhibits statistically significant persistence in all ETP asset classes

Risk Sentiment Flow = (High – Low Risk Flowk ) / StdDev(Net Flowk)


05 06 07 08 09 10 11 12 13 14-100

-50

0

50Equity ETPs

Year

Sentim

ent

Flo

w

05 06 07 08 09 10 11 12 13 14-60

-40

-20

0

20Fixed Income ETPs

Year

Sentim

ent

Flo

w

05 06 07 08 09 10 11 12 13 14-20

-10

0

10

20Commodities ETPs

Year

Sentim

ent

Flo

w

*** Denotes statistical significance at 0.1%

** Denotes statistical significance at 1%

* Denotes statistical significance at 5%


Part Two: Liquidity and Price Discovery in ETFs


BlackRock

ETFs in Global Financial Markets

Key objectives and questions:

• Clarify common misconceptions about ETF prices, premiums, and liquidity.

• Provide sound quantitative view into the role that ETFs play as price discovery tools in global financial markets

• Can the dynamics of ETF prices, volatilities, and premiums be described through systematic econometric framework?

• Are ETFs efficiently priced?

• What is the role of liquidity in pricing ETFs?

• What are the key drivers behind ETF premiums and how do they change with the nature of the ETF exposure (asset class,

geography)?

• Is there a persistence in ETF premiums?


Key Drivers of ETP Market and NAV prices

𝑝𝑡 = 𝑚𝑡 + 𝑢𝑡

𝑢𝑡 = 𝜑𝑢𝑡−1 + 𝜖𝑡

𝑛𝑡 = 1 − 𝜃 𝑚𝑡 + 𝜃𝑛𝑡−1 + 𝛾𝑡

𝑑𝑚𝑡 = 𝑚𝑡 − 𝑚𝑡−1 = 𝐶 + 𝛿𝑡

ETF market price pt is the sum of true (unobserved) asset price mt and liquidity shocks (noise) ut:

True (unobserved) asset price mt follows a martingale process:

Error correction in liquidity shocks ut is modeled as AR(1) process:

Net Asset Value (NAV) (denoted as nt) can deviate from true asset price because of various pricing errors gt:

Staleness parameter q > 0 indicates to what degree stale NAV quotes were used to determine current NAV.

To better understand ETF price dynamics, we specifically model one type of error, staleness, arising from

using stale quotes in calculation of NAV:

𝑛𝑡 = 𝑚𝑡 + 𝛾𝑡

* For more extensive theoretical analysis, see:

Madhavan (2013) or Engle & Sarkar (2002)


ETF Transaction Costs and Spreads


Source: Bloomberg,

BlackRock, and

FINRA TRACE as of

June 30, 2013

𝑝𝑡 = 𝑞𝑚𝑖𝑑,𝑡 +𝑐𝑡

2𝑝𝑡

The actual transaction price of the ETF at time t is the midquote qmid,t plus or minus the effective bid-ask spread ct:

𝑝𝑡 ∈ (−1,1) where

Since quotations are two-sided, it is reasonable to posit that midquote qmid,t reflects “true” asset price mt , and the

microstructure noise term ut is interpreted as (ct / 2) pt.

For an individual security, in the absence of other costs, the spread arises because order flow is informative and

market makers protect themselves against adverse selection.

In the context of ETF, the fact that a broad index portfolio is being traded, flow is unlikely to be informative at the

individual security level, hence expectation for lower spreads.

ETFs indeed offer lower spreads compared to underlying exposure:

Average Time-Weighted Bid-Ask Spreads (bps)

20

State-Space Model Representation of ETF Price Dynamics

The cointegrated evolution of ETF market and NAV prices can be described in State-Space Model (SSM) form:

𝑛𝑡

𝑝𝑡=

1 − 𝜃 01 −𝜑

𝑚𝑡

𝑚𝑡−1+

𝜃 00 𝜑

𝑛𝑡−1

𝑝𝑡−1+

𝛾𝑡

𝜖𝑡 SSM measurement equation:

SSM transition equation: 𝑚𝑡

𝑚𝑡−1=

1 01 0

𝑚𝑡−1

𝑚𝑡−2+

𝐶 00 0

10

+𝛿𝑡

0

ETF premium (discount) (or P/D) can be written as:

𝜋𝑡 = 𝑝𝑡 − 𝑛𝑡 = 𝑢𝑡 + 𝜃 𝑚𝑡 − 𝑛𝑡−1 − 𝛾𝑡

Assuming all innovations (e t, gt, and dt) are i.i.d., the variance of ETF premium can be approximated as:

var 𝜋 ≅ var 𝜖

1 − 𝜑2 + 𝜃2var 𝛿

1 − 𝜃2 + var(𝛾)

Transitory

Liquidity

NAV

Staleness

NAV Pricing

Errors NAV Measurements Errors (price discovery)

The last equation allows to attribute variance of P/D into portions related to transitory liquidity and price discovery.


State-Space Model Estimation: Examples

Source: Bloomberg, BlackRock

for period 1/1/2005 – 12/31/2013

Analyzed three US-listed ETF funds (IVV, EWJ, and HYG) using daily price and NAV data for period

1/1/2005 through 12/31/2013

Model is solved in Matlab using Kalman Filter and maximum likelihood estimation.

ETF Ticker IVV EWJ HYG

ETF Name iShares S&P500

ETF

iShares MSCI Japan

ETF

iShares iBoxx High

Yield Bond ETF

q (NAV Staleness) -0.015 0.325 0.772

j (Autocorrelation) 0.109 0.179 0.857

Fundamental Innovations: St.Dev.(d) (annualized) 0.207 0.192 0.139

Price Innovation: St.Dev.(e) (annualized) 0.011 0.099 0.087

NAV Innovations: St.Dev.(g) (annualized) 0.015 0.145 0.046

Realized St.Dev.(P/D) (annualized) 0.019 0.200 0.230

Realized St.Dev.(Px) (annualized) 0.208 0.238 0.150

Realized St.Dev.(NAV) (annualized) 0.212 0.232 0.070

% Realized P/D variance explained by Transitory Liquidity 35.5% 25.2% 54.3%

% Realized P/D variance explained by NAV Staleness 2.6% 10.9% 54.0%

% Realized P/D variance explained by NAV Pricing Errors 61.4% 52.8% 4.1%


Drivers of ETF Premiums: Domestic Equity ETFs


for period 1/1/2005 – 12/31/2013

Analyzed all US-listed, domestic equity ETF funds with above $100MM in AUM (as of 12/31/2013) using

daily price and NAV data for period 1/1/2005 through 12/31/2013



Domestic Equity ETFs

% Contribution to P/D Variance

Mean AUM

Weighted

Transitory Liquidity 55.5% 52.3%

NAV Staleness 7.6% 3.7%

NAV Price Errors 37.2% 44.0%

0 50 100 150 20010

2

103

104

105

ETF AUM ($MM, Log-scale)

0 50 100 150 2000

10

20P/D Volatility (%)

0 50 100 150 2000

0.5

1

ETF (ranked from the highest to lowest in AUM)

Fraction P/D Variance Explained by SSM

Px LiquidNAV Stale

NAV Error

23

Drivers of ETF Premiums: Developed Markets (ex-US) Equity ETFs

Analyzed all US-listed developed markets (ex-US) equity ETF funds with above $100MM in AUM (as of 12/31/2013)

using daily price and NAV data for period 1/1/2005 through 12/31/2013




for period 1/1/2005 – 12/31/2013

0 10 20 30 40 50 6010

2

103

104

105


0 10 20 30 40 50 600

20


0 10 20 30 40 50 600

0.5

1



Px LiquidNAV Stale

NAV Error

Developed Markets (ex-US) Equity ETFs


Mean AUM

Weighted




24

Drivers of ETF Premiums: Emerging Markets Equity ETFs

Analyzed all US-listed emerging markets equity ETF funds with above $100MM in AUM (as of 12/31/2013)

using daily price and NAV data for period 1/1/2005 through 12/31/2013




for period 1/1/2005 – 12/31/2013

Emerging Markets Equity ETFs


Mean AUM

Weighted




0 10 20 30 40 5010

2

103

104

105


0 10 20 30 40 500

25


0 10 20 30 40 500

0.5

1



Px LiquidNAV Stale

NAV Error

25

Summary and Conclusions

Contributions to Premium/Discount Variance

Source: Bloomberg, BlackRock, daily data for period 1/1/2005 – 12/31/2013.

Includes all US-listed ETFs with more than $100MM in AUM as of 12/31/2013


Summary of key findings:

• Described ETF prices, volatilities, and premiums in State-Space Model (SSM) representation.

• Key drivers of ETF premiums identified as:

• Transitory liquidity observed ETF market prices (i.e. bid-ask bounce, or liquidity shocks);

• Staleness and other error measurements in NAV prices.

• Attributed variance of premiums and discounts into liquidity and NAV error measurements for various categories of ETFs

• Provided quantitative argument for ETFs serving as price discovery tools, particularly for international ETFs

0%

25%

50%

75%

100%

Domestic Equity DM (ex-US) Equity EM Equity

% Transitory Liquidity % NAV Staleness % Nav Price Error

26

Thank you


BlackRock

Carefully consider the iShares Funds’ investment objectives, risk factors, and charges and expenses before

investing. This and other information can be found in the Funds’ prospectuses, which may be obtained by calling 1-

800-iShares (1-800-474-2737) or by visiting www.iShares.com. Read the prospectus carefully before investing.

Investing involves risk, including possible loss of principal.

Transactions in shares of ETFs will result in brokerage commissions and will generate tax consequences. All regulated

investment companies are obliged to distribute portfolio gains to shareholders.

Although market makers will generally take advantage of differences between the NAV and the trading price of iShares Fund

shares through arbitrage opportunities, there is no guarantee that they will do so.


The iShares Funds are distributed by BlackRock Investments, LLC (together with its affiliates, “BlackRock”).

The iShares Funds are not sponsored, endorsed, issued, sold or promoted by Cohen & Steers Capital Management, Inc.,

European Public Real Estate Association (“EPRA® ”), FTSE International Limited (“FTSE”), India Index Services & Products

Limited, JPMorgan Chase & Co., MSCI Inc., Markit Indices Limited, Morningstar, Inc., The NASDAQ OMX Group, Inc.,

National Association of Real Estate Investment Trusts (“NAREIT”), New York Stock Exchange, Inc., Russell Investment Group

or S&P Dow Jones Indices LLC, nor are they sponsored, endorsed or issued by Barclays Capital Inc. None of these

companies make any representation regarding the advisability of investing in the Funds. BlackRock is not affiliated with the

companies listed above.

©2014 BlackRock. All rights reserved. iSHARES and BLACKROCK are registered trademarks of BlackRock. All other marks

are the property of their respective owners. iS-12030-0314

Not FDIC Insured • No Bank Guarantee • May Lose Value

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ETF Flow Analysis - MathWorks